Turning to more conceptual questions, an interesting puzzle is how to deal with eternal inflation. In particular, the “measure problem”: how should we compute probabilities in eternal inflation?
A closely related question is whether there is a wavefunction of the universe, and if so how it might be computed. This is an area which seems to need a deeper input from quantum gravity, since there are proposals that vary widely. The most mathematically elegant is the Hartle-Hawking proposal, which unfortunately seems to be in contradiction with experiment. Along these lines there have been attempts to extend lessons from AdS/CFT to de Sitter space, but we are lacking a sufficiently explicit holographic example which leads to a standard Einstein-like gravity in the bulk. It seems likely that some of the recent progress in the description of quantum black holes [1]} could have implications for cosmology, and we now turn to this subject.
